Example Question - cone volume formula
Here are examples of questions we've helped users solve.
Calculating the Volume of a Cone
The volume of a cone can be calculated using the formula: \[ \text{Volume} = \frac{1}{3} \pi r^2 h \] Where \( r \) is the radius of the base of the cone and \( h \) is the height of the cone. For a cone with a height \( h = 20 \) cm and a base radius \( r = 10 \) cm, we can plug these values into the formula to get the volume: \[ \text{Volume} = \frac{1}{3} \pi \times (10 \text{ cm})^2 \times 20 \text{ cm} \] The correct formula to use for the calculation, based on the given information and the options provided in the image, is the third one: \[ \boxed{\frac{1}{3} \pi \times (10 \times 10) \times 20} \]
Calculating height of cone given volume and radius
The volume of a cone is given by the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cone. Here, we are given: \[ V = 37.68 \, \text{cubic centimeters} \] \[ r = 3 \, \text{centimeters} \] \[ \pi \approx 3.14 \] Let's solve for \( h \): \[ 37.68 = \frac{1}{3} \times 3.14 \times 3^2 \times h \] \[ 37.68 = \frac{1}{3} \times 3.14 \times 9 \times h \] \[ 37.68 = 3.14 \times 3 \times h \] \[ 37.68 = 9.42 \times h \] \[ h = \frac{37.68}{9.42} \] \[ h \approx 4 \] Rounding to the nearest hundredth, \( h \) would then be \( 4.00 \) centimeters.
Calculating the Volume of a Cone
To find the volume of a cone, you can use the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius of the base of the cone, and \( h \) is the height of the cone. Given that the radius \( r = 3 \) cm and the height \( h = 4 \) cm, you can plug these values into the formula: \[ V = \frac{1}{3} \pi (3\, \text{cm})^2 (4\, \text{cm}) \] \[ V = \frac{1}{3} \pi \cdot 9\, \text{cm}^2 \cdot 4\, \text{cm} \] \[ V = \frac{1}{3} \pi \cdot 36\, \text{cm}^3 \] \[ V = 12 \pi\, \text{cm}^3 \] So the volume of the cone is \( 12 \pi \) cubic centimeters.
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